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Journal of Environmental Accounting and Management 12(2) (2024) 129--139 | DOI:10.5890/JEAM.2024.06.002

Thilini V. Mahanama$^1$, Pushpi Paranamana$^2$, Dimitri Volchenkov$^3$

$^1$ Department of Industrial Management, Faculty of Science, University of Kelaniya, Kelaniya, 11600, Sri Lanka

$^2$ Department of Mathematics & Computer Science, Saint Mary's College, IN 46556, USA

$^3$ Department of Mathematics & Statistics, Texas Tech University, Lubbock TX 79409-1042, USA

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Abstract

We examine the relationship between property losses caused by tornadoes and their physical parameters, namely the tornado path length and width, using data reported by the National Oceanic and Atmospheric Administration in the United States.~We observe that the statistics of property losses cannot be described by a single distribution but rather by a two-dimensional statistical manifold of distributions that may reflect two different mechanisms of property loss compensations. Assessing the difference between distributions of losses caused by tornadoes using Kolmogorov-Smirnov's distance, we construct the 2-D manifold using the method of multi-dimensional scaling. Then we define a “curvature coefficient” that characterizes the contraction and expansion of the derived manifold to explain the complex dynamics of the probability distributions of losses. The regions with expansions identify the ranges of physical parameters for which the extreme tornado events may occur, which helps in assessing compensation strategies.

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